Question

How do you graph the equation `2x-8y=-15`?

Answer 1

See a solution below:

Explanation:

First, we can determine two points on the line by finding the `x` and `y` intercepts by setting one variable to `0` and then solve for the other variable:

x-intercept

`2x - (8 * 0) = -15`

`2x - 0 = -15`

`2x = -15`

`(2x)/color(red)(2) = -15/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -15/2`

`x = -15/2` or `(-15/2,0)`

y-intercept

`(2 * 0) - 8y = -15`

`0 - 8y = -15`

`-8y = -15`

`(-8y)/color(red)(-8) = (-15)/color(red)(-8)`

`(color(red)(cancel(color(black)(-8)))y)/cancel(color(red)(-8)) = 15/8`

`y = 15/8` or `(0, 15/8)`

We can next plot these two points:

graph{((x+ (15/2))^2+(y)^2-0.125)((x)^2+(y-(15/8))^2-0.125)=0 [-20, 20, -10, 10]}

Now, we can draw a line through the two points giving:

graph{(2x - 8y + 15)((x+ (15/2))^2+(y)^2-0.125)((x)^2+(y-(15/8))^2-0.125)=0 [-20, 20, -10, 10]}